The present invention relates generally to the sampling of particle-laden fluids for particulate content and particle size distribution and more particularly to a specific way of accomplishing this utilizing a cascade impactor having specifically designed collection stages.
As will be seen hereinafter, the overall particle sampling assembly provided in accordance with a preferred embodiment of the present invention utilizes a cascade impactor of the type disclosed in U.S. Pat. No. 3,693,457 which issued to M. J. Pilat on Sept. 26, 1972. This impactor, as disclosed in the patent, includes a longitudinally extending, tubular body having a fluid inlet and a fluid outlet and a plurality of longitudinally spaced, successive particle collection stages located within the tubular body between its inlet and outlet ends. In the cascade impactor, thus far described, the stream of fluid to be sampled, for example, the stream of particle-laden exhaust gases from a pool of coal burning steam generator or the like, is passed through apertured jet plates in successive collection stages where particles of diminishing sizes are respectively captured on collection plates respectively positioned in confronting relation with the jet plates, as discussed in more detail in the Pilat patent.
The cascade impactor just described comprises part of an overall assembly train including a filter at the outlet of the impactor as well as a dry gas meter including pressure gauges and a vacuum pump downstream therefrom. This assembly may also include a downstream condensor (not specifically illustrated in the Pilat patent) and impingers within a constant temperature bath (illustrated in the Pilat patent) located upstream of the dry gas meter for preventing moisture from entering the meter.
A more recent development in the overall assembly just described has been the addition of a second cascade impactor operatively positioned downstream of the impactor described, that is, between the outlet end of the first impactor and the downstream filter recited above. This second or downstream cascade impactor is similar to the impactor described above in that it includes a longitudinally extending, tubular body having an inlet and an outlet as well as a number of successive particle collection stages located within the tubular body between its inlet and outlet. However, the pressure across the successive stages of this latter impactor, rather than being relatively constant from its inlet to its outlet as in the cascade impactor described above, decreases in pressure from stage to stage which was briefly alluded to in the Pilat patent. The primary reason for providing pressure drops between successive particle collection stages in this second or downstream impactor is so that the latter is capable of collecting substantially smaller particles, for example, those in the submicron range, specifically those which are in the range of 0.2 microns in diameter.
In order to more fully understand the present invention, it is important to briefly discuss the theory behind the cascade impactors described herein, even though a similar discussion was provided in the Pilat patent. The cascade impactor thus far described, whether it is the initial upstream impactor or the second downstream impactor, fractionates the particulate matter within the particle-laden fluid stream into size increments by inertial impaction of the particles on a collection surface. This occurs at successive stages within the impactor and the resulting index of particle size is traditionally expressed by the particle size collected within 50% collection efficiency for each stage, typically referred to as the "d.sub.50 ". The particle diameter has been related to the Stokes inertial impaction parameter .PSI. which is defined by Ranz and Wong (1952) as ##EQU1## where C is the Cunningham correction factor, .rho. the particle density, d.sub.p the particle diameter, V.sub.j the gas velocity in the jet, .mu. the gas viscosity and D.sub.j the jet diameter. Solutions of the equation of particle motion at various magnitudes of 1/8 and experimental studies have shown that the Stokes inertial impaction parameter at 50% collection efficiency (.PSI.50) for a particular diameter (d.sub.50) ranges between 0.12 and 0.17 for circular jets. These values were originally reported by Ranz and Wong (1952) and later confirmed by McFarland and Zeller (1963). Solving for the particle diameter from equation 1 gives ##EQU2## Substituting an average value of 0.145 for .PSI..sub.50 provides an equation for d.sub.50, ##EQU3## Equation 3 provides an expression which relates the cascade impactor stage d.sub.50 and the impactor parameters. These parameters can be appropriately altered to provide an even distribution of d.sub.50's throughout the impactor stages. For sizing of submicron particles, the Cunningham correction factor becomes of particular significance due to the physical limitations in further altering the other impactor parameters. The Cunningham correction factor C is defined by an equation reported by Davies (1945) ##EQU4## where .lambda. is the gas mean free path. The relationship of the Cunningham correction factor to the absolute gas pressure for various particle diameters is illustrated in FIG. 1. Thus it can be seen by examination of equations 3 and 4 and FIG. 1 that it is possible to select the appropriate magnitudes of the impactor parameters necessary to provide a stage d.sub.50 as low as 0.02 microns. Assuming a particle density .pi. of 1.0 gram/cm.sup.3 and substituting into equation 3 provides an equation for the aerodynamic cut diameter da.sub.50 ##EQU5##
In summarizing the foregoing with particular reference to equation 5, it should be quite apparent that the size (da.sub.50) of particles collected at any given stage of the impactor is dependent on the diameter of the apertures through the jet plate in that stage (the jet diameter D.sub.j), the viscosity of the fluid passing throughthe jet hole (the gas viscosity .mu.), as well as the velocity of the fluid through the jet (V.sub.j) and the Cunningham correction factor (C) as discussed above. Obviously, the gas viscosity is fixed and the jet diameter is fixed, thereby leaving only the Cunningham correction factor C which might vary (with pressure) and the jet velocity which is known to depend on the flow rate (a possible variable) through the apertures as well as the jet diameter (a constant) and the number of apertures (also a constant). Accordingly, in order to accurately monitor the da.sub.50 at any given state, it is necessary to continuously monitor the Cunningham correction factor (a possible variable) and the jet velocity (another possible variable). In order to monitor the Cunningham correction factor, it is necessary to monitor the pressure at that stage which can be calibrated in terms of the Cunningham correction factor using the information in the graph of FIG. 1 and/or equation 4. While it is possible to monitor the velocity of gas through the various apertures in the jet plate, this would disrupt the jet stream through the impactor. However, since the number of apertures in the plate is known and their size, it is only necessary to monitor the overall flow rate through the impactor for converting this information to jet velocity through any given aperture plate.
In view of the foregoing, the overall particle sampling assembly including the cascade impactor of the type just described also includes an arrangement for monitoring the pressure at each collection stage thereof. This arrangement has heretofore included a plurality of gas tubes, one for each stage, extending from the various impactor stages to a remote location, specifically to a location where the operator maintains his control equipment. Typically, the operator would monitor the various stages, one at a time, utilizing some sort of conventional pressure gauge.
It should be quite apparent that the monitoring procedure just described is time-consuming and tedious. Moreover, it is quite possible for the operator to inaccurately record the pressure values which are successively taken from stage to stage, thereby resulting in an inaccurate Cunningham correction factor. In addition, because the cascade impactor may include a relatively large number of stages, for example, as many as 28, it necessarily includes an equal number of pressure sampling tubes leading from the impactor to the relatively remote control station. This not only adds cost to the overall assembly and is quite inconvenient, especially when the sampling procedure is carried out in relatively close quarters, but in some cases, the space requirements are not at all sufficiently flexible (regardless of convenience) to allow a large number of pressure sampling conduits to extend between the impactor and control station.
As will be seen hereinafter, the overall particle sampling assembly of the present invention does not monitor the various collection stages using a single pressure gauge, and it does not utilize relatively inflexible fluid carrying conduits extending between the impactor and control station. Rather, as will also be seen, the overall assembly of the present invention monitors the pressure at the various stages simultaneously and continuously throughout the assembly operation, utilizing transducers located at the impactor for converting the pressure at each stage to a corresponding electrical signal. These signals are carried back to the remote control station by flexible electrical cables which can readily adapt to the space requirements and which are relatively convenient for the operator. At the control station, these signals can be readily converted electronically to visual and/or permanent readouts (either stage-by-stage or simultaneous readouts) and they may be appropriately calibrated to readout in the form of the Cunningham correction factor without requiring conversion by the operator.
From the foregoing, the importance of accurately monitoring the Cunningham correction factor for accurately determining the da.sub.50 at any given detection stage should be quite apparent. However, it is equally important to prevent the rate of flow of the fluid from one stage to the next (through successive jet plates) from reaching its Critical Flow Rate (CFR). Briefly stated, CFR is the rate at which the velocity of the fluid passing from one stage to the next downstream stage does not increase with a drop in pressure (within practical limits) from the upstream stage to the next downstream stage. In the past, this was accomplished by designing the various collection stages to have a mach number such that the jet stream through any specific aperture was subsonic. However, Applicants have discovered that this does not reliably prevent the rate of flow of the fluid stream from reaching its Critical Flow Rate. Accordingly, the Cunningham correction factor at one stage of the cascade impactor may be different than the Cunningham correction factor at the next stage while the jet velocity at each stage is the same (because the flow rate between the two has reached its CFR level). This, of course, ultimately leads to inaccuracies in the da.sub.50 at the downstream collection plate since the velocity onto that plate is not truly what it should be based on its lower pressure (compared to the upstream stage).
As will be seen hereinafter, the cascade impactor constructed in accordance with the present invention is designed in a more reliable way to prevent the rate of flow of the fluid stream from one stage to the next from reaching CFR and thus assuring that the jet velocity for any particular aperture between these stages is truly indicative of the pressure drop across that stage. As will also be seen, this is accomplished by designing the apertures in any given gas jet plate to be below a predetermined ratio of pressure at its upstream side (within the upstream stage) as compared to the pressure on its downstream side (the pressure within the downstream stage). The ratio selected is one known in the art, specifically the Critical Pressure Ratio (CPR) below which the gas flows through the apertures at a rate below its CFR level. This ratio as will be discussed is a constant, specifically about 1.71.